diff --git a/src/compiler/commandLineParser.ts b/src/compiler/commandLineParser.ts
index 9797d9f96cc66..c596372563ff4 100644
--- a/src/compiler/commandLineParser.ts
+++ b/src/compiler/commandLineParser.ts
@@ -1176,6 +1176,15 @@ const commandOptionsWithoutBuild: CommandLineOption[] = [
         defaultValueDescription: false,
         transpileOptionValue: undefined,
     },
+    {
+        name: "rewriteRelativeImportExtensions",
+        type: "boolean",
+        affectsSemanticDiagnostics: true,
+        affectsBuildInfo: true,
+        category: Diagnostics.Modules,
+        description: Diagnostics.Rewrite_ts_tsx_mts_and_cts_file_extensions_in_relative_import_paths_to_their_JavaScript_equivalent_in_output_files,
+        defaultValueDescription: false,
+    },
     {
         name: "resolvePackageJsonExports",
         type: "boolean",
diff --git a/src/compiler/diagnosticMessages.json b/src/compiler/diagnosticMessages.json
index 6f5d7ada6c028..24344f564b0cd 100644
--- a/src/compiler/diagnosticMessages.json
+++ b/src/compiler/diagnosticMessages.json
@@ -5934,6 +5934,10 @@
         "category": "Message",
         "code": 6420
     },
+    "Rewrite '.ts', '.tsx', '.mts', and '.cts' file extensions in relative import paths to their JavaScript equivalent in output files.": {
+        "category": "Message",
+        "code": 6421
+    },
 
     "The expected type comes from property '{0}' which is declared here on type '{1}'": {
         "category": "Message",
diff --git a/src/compiler/moduleNameResolver.ts b/src/compiler/moduleNameResolver.ts
index 850a8a7f381cb..35ea6c970f7e6 100644
--- a/src/compiler/moduleNameResolver.ts
+++ b/src/compiler/moduleNameResolver.ts
@@ -36,6 +36,7 @@ import {
     forEach,
     forEachAncestorDirectory,
     formatMessage,
+    getAllowImportingTsExtensions,
     getAllowJSCompilerOption,
     getAnyExtensionFromPath,
     getBaseFileName,
@@ -3303,7 +3304,7 @@ function resolveFromTypeRoot(moduleName: string, state: ModuleResolutionState) {
 // so this function doesn't check them to avoid propagating errors.
 /** @internal */
 export function shouldAllowImportingTsExtension(compilerOptions: CompilerOptions, fromFileName?: string) {
-    return !!compilerOptions.allowImportingTsExtensions || fromFileName && isDeclarationFileName(fromFileName);
+    return getAllowImportingTsExtensions(compilerOptions) || fromFileName && isDeclarationFileName(fromFileName);
 }
 
 /**
diff --git a/src/compiler/program.ts b/src/compiler/program.ts
index 198dfa0975457..2808587f7ca49 100644
--- a/src/compiler/program.ts
+++ b/src/compiler/program.ts
@@ -4523,7 +4523,7 @@ export function createProgram(rootNamesOrOptions: readonly string[] | CreateProg
             }
         }
 
-        if (options.allowImportingTsExtensions && !(options.noEmit || options.emitDeclarationOnly)) {
+        if (options.allowImportingTsExtensions && !(options.noEmit || options.emitDeclarationOnly || options.rewriteRelativeImportExtensions)) {
             createOptionValueDiagnostic("allowImportingTsExtensions", Diagnostics.Option_allowImportingTsExtensions_can_only_be_used_when_either_noEmit_or_emitDeclarationOnly_is_set);
         }
 
diff --git a/src/compiler/transformers/ts.ts b/src/compiler/transformers/ts.ts
index 036b8d60f9f27..d21ec42f16911 100644
--- a/src/compiler/transformers/ts.ts
+++ b/src/compiler/transformers/ts.ts
@@ -12,6 +12,7 @@ import {
     Bundle,
     CallExpression,
     CaseBlock,
+    changeExtension,
     childIsDecorated,
     ClassDeclaration,
     ClassElement,
@@ -55,6 +56,7 @@ import {
     getInitializedVariables,
     getIsolatedModules,
     getOriginalNode,
+    getOutputExtension,
     getParseTreeNode,
     getProperties,
     getStrictOptionValue,
@@ -81,6 +83,7 @@ import {
     isClassElement,
     isClassLike,
     isComputedPropertyName,
+    isDeclarationFileName,
     isDecorator,
     isElementAccessExpression,
     isEntityName,
@@ -122,6 +125,7 @@ import {
     isSimpleInlineableExpression,
     isSourceFile,
     isStatement,
+    isStringLiteral,
     isTemplateLiteral,
     isTryStatement,
     JsxOpeningElement,
@@ -155,6 +159,7 @@ import {
     parameterIsThisKeyword,
     ParameterPropertyDeclaration,
     ParenthesizedExpression,
+    pathIsRelative,
     PropertyAccessExpression,
     PropertyDeclaration,
     PropertyName,
@@ -2269,12 +2274,22 @@ export function transformTypeScript(context: TransformationContext) {
                 node,
                 /*modifiers*/ undefined,
                 importClause,
-                node.moduleSpecifier,
+                rewriteModuleSpecifier(node.moduleSpecifier),
                 node.attributes,
             )
             : undefined;
     }
 
+    function rewriteModuleSpecifier(node: Expression): Expression;
+    function rewriteModuleSpecifier(node: Expression | undefined): Expression | undefined;
+    function rewriteModuleSpecifier(node: Expression | undefined): Expression | undefined {
+        if (!node || !compilerOptions.rewriteRelativeImportExtensions || !isStringLiteral(node) || !pathIsRelative(node.text) || isDeclarationFileName(node.text)) {
+            return node;
+        }
+        const updatedText = changeExtension(node.text, getOutputExtension(node.text, compilerOptions));
+        return updatedText !== node.text ? setOriginalNode(setTextRange(factory.createStringLiteral(updatedText, node.singleQuote), node), node) : node;
+    }
+
     /**
      * Visits an import clause, eliding it if its `name` and `namedBindings` may both be elided.
      *
@@ -2342,7 +2357,14 @@ export function transformTypeScript(context: TransformationContext) {
             // never elide `export <whatever> from <whereever>` declarations -
             // they should be kept for sideffects/untyped exports, even when the
             // type checker doesn't know about any exports
-            return node;
+            return factory.updateExportDeclaration(
+                node,
+                node.modifiers,
+                node.isTypeOnly,
+                node.exportClause,
+                rewriteModuleSpecifier(node.moduleSpecifier),
+                node.attributes,
+            );
         }
 
         // Elide the export declaration if all of its named exports are elided.
@@ -2359,7 +2381,7 @@ export function transformTypeScript(context: TransformationContext) {
                 /*modifiers*/ undefined,
                 node.isTypeOnly,
                 exportClause,
-                node.moduleSpecifier,
+                rewriteModuleSpecifier(node.moduleSpecifier),
                 node.attributes,
             )
             : undefined;
@@ -2421,8 +2443,24 @@ export function transformTypeScript(context: TransformationContext) {
         }
 
         if (isExternalModuleImportEqualsDeclaration(node)) {
-            const isReferenced = shouldEmitAliasDeclaration(node);
-            return isReferenced ? visitEachChild(node, visitor, context) : undefined;
+            if (!shouldEmitAliasDeclaration(node)) {
+                return undefined;
+            }
+            const updatedModuleSpecifier = rewriteModuleSpecifier(node.moduleReference.expression);
+            if (updatedModuleSpecifier !== node.moduleReference.expression) {
+                return visitEachChild(
+                    factory.updateImportEqualsDeclaration(
+                        node,
+                        node.modifiers,
+                        node.isTypeOnly,
+                        node.name,
+                        factory.updateExternalModuleReference(node.moduleReference, updatedModuleSpecifier),
+                    ),
+                    visitor,
+                    context,
+                );
+            }
+            return visitEachChild(node, visitor, context);
         }
 
         if (!shouldEmitImportEqualsDeclaration(node)) {
diff --git a/src/compiler/types.ts b/src/compiler/types.ts
index ec5aa60564eac..8d11378287a57 100644
--- a/src/compiler/types.ts
+++ b/src/compiler/types.ts
@@ -7443,6 +7443,7 @@ export interface CompilerOptions {
     removeComments?: boolean;
     resolvePackageJsonExports?: boolean;
     resolvePackageJsonImports?: boolean;
+    rewriteRelativeImportExtensions?: boolean;
     rootDir?: string;
     rootDirs?: string[];
     skipLibCheck?: boolean;
diff --git a/src/compiler/utilities.ts b/src/compiler/utilities.ts
index fb4da5887538d..cc9308f0cf6e6 100644
--- a/src/compiler/utilities.ts
+++ b/src/compiler/utilities.ts
@@ -8821,6 +8821,12 @@ function createComputedCompilerOptions<T extends Record<string, CompilerOptionKe
 
 /** @internal */
 export const computedOptions = createComputedCompilerOptions({
+    allowImportingTsExtensions: {
+        dependencies: ["rewriteRelativeImportExtensions"],
+        computeValue: compilerOptions => {
+            return !!(compilerOptions.allowImportingTsExtensions || compilerOptions.rewriteRelativeImportExtensions);
+        },
+    },
     target: {
         dependencies: ["module"],
         computeValue: compilerOptions => {
@@ -9046,6 +9052,8 @@ export const computedOptions = createComputedCompilerOptions({
     },
 });
 
+/** @internal */
+export const getAllowImportingTsExtensions = computedOptions.allowImportingTsExtensions.computeValue;
 /** @internal */
 export const getEmitScriptTarget = computedOptions.target.computeValue;
 /** @internal */